What is the integral of (3-5x)sqrt(x) ?

The integral of (3-5x)sqrt(x) is 2x^{3/2}-2x^{5/2}+C

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integral of (3-5x)sqrt(x)

\int (3 - 5 x) x d x

2 x^{\frac{3}{2}} - 2 x^{\frac{5}{2}} + C

Solution steps

\int (3 - 5 x) x d x

Expand

(3 - 5 x) x : 3 x - 5 x^{\frac{3}{2}}

= \int 3 x - 5 x^{\frac{3}{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 x d x - \int 5 x^{\frac{3}{2}} d x

\int 3 x d x = 2 x^{\frac{3}{2}}

\int 5 x^{\frac{3}{2}} d x = 2 x^{\frac{5}{2}}

= 2 x^{\frac{3}{2}} - 2 x^{\frac{5}{2}}

Add a constant to the solution

= 2 x^{\frac{3}{2}} - 2 x^{\frac{5}{2}} + C

\int (1 + tan (x))^{2} \cdot sec (x) d x

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What is the integral of (3-5x)sqrt(x) ?
The integral of (3-5x)sqrt(x) is 2x^{3/2}-2x^{5/2}+C